A012572 exp(arcsinh(x)*log(x+1))=1+2/2!*x^2-3/3!*x^3+16/4!*x^4-80/5!*x^5...

1, 0, 2, -3, 16, -80, 488, -3339, 26472, -241128, 2416002, -26168835, 310984452, -4057771068, 56774212350, -841821751575, 13356966503088, -227284196307984, 4085254725230514, -76911822855270819

Offset: 0

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Keywords

• sign

Programs

Mathematica

CoefficientList[Series[Exp[ArcSinh[x]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 31 2013 *)

Formula

E.g.f.: (x+sqrt(1+x^2))^(log(x+1)). - Vaclav Kotesovec, Oct 31 2013

a(n) ~ n! * (-1)^n * n^(log(1+sqrt(2))-1) / GAMMA(log(1+sqrt(2))). - Vaclav Kotesovec, Oct 31 2013